How to swap Y and Z axis on export to Collada
No. Blender's Collada exporter does not have a convenient way to do this. Your best option is to rotate the object as you mentioned.

Note that just rotating the object might be insufficient for some applications, e.g those which actually care about Collada's up-axis specification (which can be either Z_UP or Y_UP).

If you're working with one of those, you'll also need to manually edit the exported file.